16.8 DIFFERENTIAL PROTECTION
The restricted earth fault schemes described above in Section 16.7 depend entirely
on the Kirchhoff principle that the sum of the currents flowing into a conducting
network is zero. A differential system can be arranged to cover the complete
transformer; this is possible because of the high efficiency of transformer
operation, and the close equivalence of ampere-turns developed on the primary and
secondary windings. Figure 16.7 illustrates the principle.
Current transformers on the primary and secondary sides are connected to form a
circulating current system.
16.8.1 Basic Considerations for Transformer Differential Protection
In applying the principles of differential protection to transformers, a variety of
considerations have to be taken into account. These include:
a. correction for possible phase shift across the transformer windings (phase
correction)
b. the effects of the variety of earthing and winding arrangements (filtering of zero
sequence currents)
c. correction for possible unbalance of signals from current transformers on either
side of the windings (ratio correction)
d. the effect of magnetising inrush during initial energisation
e. the possible occurrence of overfluxing
In traditional transformer differential schemes, the requirements for phase and ratio
correction were met by the application of external interposing current transformers
(ICT’s), as a secondary replica of the main winding connections, or by a delta
connection of the main CT’s to provide phase correction only.
Digital/numerical relays implement ratio and phase correction in the relay software
instead, thus enabling most combinations of transformer winding arrangements to
be catered for, irrespective of the winding connections of the primary CT’s. This
avoids the additional space and cost requirements of hardware interposing CT’s.
16.8.2 Line Current Transformer Primary Ratings
Line current transformers have primary ratings selected to be approximately equal
to the rated currents of the transformer windings to which they are applied.

Primary ratings will usually be limited to those of available standard ratio CT’s.
16.8.3 Phase Correction
Correct operation of transformer differential protection requires that the
transformer primary and secondary currents, as measured by the relay, are in phase.
If the transformer is connected delta/star, as shown in Figure 16.8, balanced three-
phase through current suffers a phase change of 30°. If left uncorrected, this phase
difference would lead to the relay seeing through current as an unbalanced fault
current, and result in relay operation. Phase correction must be implemented.
Electromechanical and static relays use appropriate CT/ICT connections to ensure
that the primary and secondary currents applied to the relay are in phase.
For digital and numerical relays, it is common to use starconnected line CT’s on all
windings of the transformer and compensate for the winding phase shift in
software.
Depending on relay design, the only data required in such circumstances may be
the transformer vector group designation. Phase compensation is then performed
automatically. Caution is required if such a relay is used
to replace an existing electromechanical or static relay, as the primary and
secondary line CT’s may not have the same winding configuration. Phase
compensation and associated relay data entry requires more detailed consideration
in such circumstances. Rarely, the available phase compensation facilities cannot
accommodate the transformer winding connection, and in such cases interposing
CT’s must be used.
16.8.4 Filtering of Zero Sequence Currents
As described in Chapter 10.8, it is essential to provide some form of zero sequence
filtering where a transformer winding can pass zero sequence current to an external
earth fault. This is to ensure that out-of-zone earth faults are not seen by the
transformer protection as an in-zone fault. This is achieved by use of delta-
connected line CT’s or interposing CT’s for older relays, and hence the winding
connection of the line and/or interposing CT’s must take this into account, in
addition to any phase compensation necessary. For digital/numerical relays, the

required filtering is applied in the relay software. Table 16.4 summarises the phase
compensation and zero sequence filtering requirements. An example of an
incorrect choice of ICT connection is given in Section 16.19.1.
16.8.5 Ratio Correction
Correct operation of the differential element requires
that currents in the differential element balance under load and through fault
conditions. As the primary and secondary line CT ratios may not exactly match the
transformer rated winding currents, digital/numerical relays are provided with ratio
correction factors for each of the CT inputs. The correction factors may be
calculated automatically by the relay from knowledge of the line CT ratios and the
transformer MVA rating.
However, if interposing CT’s are used, ratio correction may not be such an easy
task and may need to take into account a factor of √ 3 if delta-connected CT’s or
ICT’s are involved. If the transformer is fitted with a tap changer, line CT ratios
and correction factors are normally chosen to achieve current balance at the mid
tap of the transformer. It is necessary to ensure that current mismatch due to off-
nominal tap operation will not cause spurious operation.
The example in Section 16.19.2 provides an illustration of how ratio correction
factors are used, and that of Section 16.9.3 shows how to set the ratio correction
factors for a transformer with an unsymmetrical tap range.
16.8.6 Bias Setting
Bias is applied to transformer differential protection for the same reasons as any
unit protection scheme – to ensure stability for external faults while allowing
sensitive settings to pick up internal faults. The situation is slightly complicated if
a tap changer is present. With line CT/ICT ratios and correction factors set to
achieve current balance at nominal tap, an off-nominal tap may be seen by the
differential protection as an internal fault.
By selecting the minimum bias to be greater than sum of the maximum tap of the
transformer and possible CT errors, maloperation due to this cause is avoided.
Some relays use a bias characteristic with three sections, as shown in Figure 16.9.

The first section is set higher than the transformer magnetising current. The second
section is set to allow for off-nominal tap settings, while the third has a larger bias
slope beginning well above rated
current to cater for heavy through-fault conditions.
16.8.7 Transformers with Multiple Windings
The unit protection principle remains valid for a system having more than two
connections, so a transformer with three or more windings can still be protected by
the application of the above principles. When the power transformer has only one
of its three windings connected to a source of supply, with the other two windings
feeding loads, a relay with only two sets of CT inputs can be used, connected as
shown in Figure 16.10(a). The separate load currents are summated in the CT
secondary circuits, and will balance with the infeed current on the supply side.
When more than one source of fault current infeed exists, there is a danger in the
scheme of Figure 16.10(a) of current circulating between the two paralleled sets of
current transformers without producing any bias. It is therefore important a relay is
used with separate CT inputs for the two secondaries - Figure 16.10(b).
When the third winding consists of a delta-connected tertiary with no connections
brought out, the transformer may be regarded as a two winding transformer for
protection purposes and protected as shown in Figure 16.10(c).
16.9 DIFFERENTIAL PROTECTION STABILISATION
DURING MAGNETISING INRUSH CONDITIONS
The magnetising inrush phenomenon described in Section 16.3 produces current
input to the energised winding which has no equivalent on the other windings.
The whole of the inrush current appears, therefore, as unbalance and the
differential protection is unable to distinguish it from current due to an internal
fault. The bias setting is not effective and an increase in the protection setting to a
value that would avoid operation would make the protection of little value.
Methods of delaying, restraining or blocking of the differential element must
therefore be used to prevent maloperation of the protection.
16.9.1 Time Delay

Since the phenomenon is transient, stability can be maintained by providing a
small time delay. However, because this time delay also delays operation of the
relay in the event of a fault occurring at switch-on, the method is no longer used.
16.9.2 Harmonic Restraint
The inrush current, although generally resembling an inzone fault current, differs
greatly when the waveforms are compared. The difference in the waveforms can be
used to distinguish between the conditions.
As stated before, the inrush current contains all harmonic orders, but these are not
all equally suitable for providing bias. In practice, only the second harmonic is
used.
This component is present in all inrush waveforms. It is typical of waveforms in
which successive half period portions do not repeat with reversal of polarity but in
which mirrorimage symmetry can be found about certain ordinates.
The proportion of second harmonic varies somewhat with the degree of saturation
of the core, but is always present as long as the uni-directional component of flux
exists. The amount varies according to factors in the transformer design. Normal
fault currents do not contain second or other even harmonics, nor do distorted
currents flowing in saturated iron cored coils under steady state conditions.
The output current of a current transformer that is energised into steady state
saturation will contain odd harmonics but not even harmonics. However, should
the current transformer be saturated by the transient component of the fault current,
the resulting saturation is not symmetrical and even harmonics are introduced into
the output current. This can have the advantage of improving the through fault
stability performance of a differential relay faults.
The second harmonic is therefore an attractive basis for a stabilising bias against
inrush effects, but care must be taken to ensure that the current transformers are
sufficiently large so that the harmonics produced by transient saturation do not
delay normal operation of the relay. The differential current is passed through a
filter that extracts the second harmonic; this component is then applied to produce
a restraining quantity sufficient to overcome the operating tendency due to the

whole of the inrush current that flows in the operating circuit. By this means a
sensitive and high-speed system can be obtained.
16.9.3 Inrush Detection Blocking
– Gap Detection Technique
Another feature that characterizes an inrush current can be seen from Figure 16.5
where the two waveforms (c) and (d) have periods in the cycle where the current is
zero. The minimum duration of this zero period is theoretically one quarter of the
cycle and is easily detected by a simple timer t1 that is set to 1/ 4f seconds.
Figure 16.11 shows the circuit in block diagram form.
Timer t1 produces an output only if the current is zero for a time exceeding 1/4f
seconds. It is reset when the instantaneous value of the differential current exceeds
the setting reference.
As the zero in the inrush current occurs towards the end of the cycle, it is necessary
to delay operation of the differential relay by 1/f seconds to ensure that the zero
condition can be detected if present. This is achieved by using a second timer t2
that is held reset by an output from timer t1.
When no current is flowing for a time exceeding 1/4f seconds, timer t2 is held reset
and the differential relay that may be controlled by these timers is blocked. When a
differential current exceeding the setting of the relay
flows, timer t1 is reset and timer t2 times out to give a trip signal in 1/f seconds. If
the differential current is characteristic of transformer inrush then timer t2 will be
reset on each cycle and the trip signal is blocked.
Some numerical relays may use a combination of the harmonic restraint and gap
detection techniques for magnetising inrush detection.
16.10 COMBINED DIFFERENTIAL
AND RESTRICTED EARTH FAULT SCHEMES
The advantages to be obtained by the use of restricted earth fault protection,
discussed in Section 16.7, lead to the system being frequently used in conjunction
with an overall differential system. The importance of this is shown in Figure
16.12 from which it will be seen that if the neutral of a star-connected winding is

earthed through a resistance of one per unit, an overall differential system having
an effective setting of 20% will detect
faults in only 42% of the winding from the line end.
Implementation of a combined differential/REF protection scheme is made easy if
a numerical relay with software ratio/phase compensation is used. All
compensation is made internally in the relay.
Where software ratio/phase correction is not available, either a summation
transformer or auxiliary CT’s can be used. The connections are shown in Figures
16.13 and 16.14 respectively.
Care must be taken in calculating the settings, but the only significant disadvantage
of the Combined Differential/REF scheme is that the REF element is likely to
operate for heavy internal faults as well as the differential elements, thus making
subsequent fault analysis somewhat confusing. However, the saving in CT’s
outweighs this disadvantage.
16.10.1 Application when an Earthing Transformer
is connected within the Protected Zone
A delta-connected winding cannot deliver any zero sequence current to an earth
fault on the connected system, any current that does flow is in consequence of an
earthed neutral elsewhere on the system and will have a 2-1-1 pattern of current
distribution between phases. When the transformer in question represents a major
power feed, the system may be earthed at that point by an earthing transformer or
earthing reactor. They are frequently connected to the system, close to the main
supply transformer and within the transformer protection zone. Zero sequence
current that flows through the earthing transformer during system earth faults will
flow through the line current transformers on this side, and, without an equivalent
current in the balancing current transformers, will cause unwanted operation of the
relays.
The problem can be overcome by subtracting the appropriate component of current
from the main CT output. The earthing transformer neutral current is used for this

purpose. As this represents three times the zero sequence current flowing, ratio
correction is required.
This can take the form of interposing CT’s of ratio 1/0.333, arranged to subtract
their output from that of the line current transformers in each phase, as shown in
Figure 16.15. The zero sequence component is cancelled, restoring balance to the
differential system.
Alternatively, numerical relays may use software to perform the subtraction,
having calculated the zero sequence component internally.
A high impedance relay element can be connected in the neutral lead between
current transformers and differential relays to provide restricted earth fault
protection to the winding.
As an alternative to the above scheme, the circulating current system can be
completed via a three-phase group of interposing transformers that are provided
with tertiary windings connected in delta. This winding effectively short-circuits
the zero sequence component and thereby removes it from the balancing quantities
in the relay circuit; see Figure 16.16.
Provided restricted earth fault protection is not required, the scheme shown in
Figure 16.16 has the advantage of not requiring a current transformer, with its
associated mounting and cabling requirements, in the neutral-earth conductor.
The scheme can also be connected as shown in Figure 16.17 when restricted earth
fault protection is needed.